Integration - A Functional Approach
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Springer Basel
1998
|
| Schriftenreihe: | Modern Birkhäuser Classics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
MARC
| LEADER | 00000nam a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV042421833 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1998 xx o|||| 00||| eng d | ||
| 020 | |a 9783034800556 |c Online |9 978-3-0348-0055-6 | ||
| 020 | |a 9783034800549 |c Print |9 978-3-0348-0054-9 | ||
| 024 | 7 | |a 10.1007/978-3-0348-0055-6 |2 doi | |
| 035 | |a (OCoLC)724768941 | ||
| 035 | |a (DE-599)BVBBV042421833 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 515.7 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Bichteler, Klaus |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Integration - A Functional Approach |c by Klaus Bichteler |
| 264 | 1 | |a Basel |b Springer Basel |c 1998 | |
| 300 | |a 1 Online-Ressource (VIII, 197 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Modern Birkhäuser Classics | |
| 500 | |a This book covers Lebesgue integration and its generalizations from Daniell's point of view, modified by the use of seminorms. Integrating functions rather than measuring sets is posited as the main purpose of measure theory. From this point of view Lebesgue's integral can be had as a rather straightforward, even simplistic, extension of Riemann's integral; and its aims, definitions, and procedures can be motivated at an elementary level. The notion of measurability, for example, is suggested by Littlewood's observations rather than being conveyed authoritatively through definitions of (sigma)-algebras and good-cut-conditions, the latter of which are hard to justify and thus appear mysterious, even nettlesome, to the beginner. The approach taken provides the additional benefit of cutting the labor in half. The use of seminorms, ubiquitous in modern analysis, speeds things up even further. The book is intended for the reader who has some experience with proofs, a beginning graduate student for example. It might even be useful to the advanced mathematician who is confronted with situations - such as stochastic integration - where the set-measuring approach to integration does not work. ------ Reviews This book provides a complete and rapid introduction to Lebesgue integration and its generalizations from Daniell’s point of view, (…) The development is clear and it contains interesting historical notes and motivations, abundant exercises and many supplements. The connection with the historical development of integration theory is also pointed out. - Zentralblatt MATH The material is well motivated and the writing is pleasantly informal. (…) There are numerous exercises, many destined to be used later in the text, and 15 pages of solutions/hints. - Mathematical Reviews | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Functional analysis | |
| 650 | 4 | |a Functional Analysis | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Riemannsches Integral |0 (DE-588)4049996-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Maßtheorie |0 (DE-588)4074626-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Integrationstheorie |0 (DE-588)4138369-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Integration |g Mathematik |0 (DE-588)4072852-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lebesgue-Integral |0 (DE-588)4034949-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Maßtheorie |0 (DE-588)4074626-4 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Integration |g Mathematik |0 (DE-588)4072852-3 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 689 | 2 | 0 | |a Integrationstheorie |0 (DE-588)4138369-2 |D s |
| 689 | 2 | |8 3\p |5 DE-604 | |
| 689 | 3 | 0 | |a Riemannsches Integral |0 (DE-588)4049996-0 |D s |
| 689 | 3 | |8 4\p |5 DE-604 | |
| 689 | 4 | 0 | |a Lebesgue-Integral |0 (DE-588)4034949-4 |D s |
| 689 | 4 | |8 5\p |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-0348-0055-6 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 3\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 4\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 5\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-027857250 | |
Datensatz im Suchindex
| DE-BY-TUM_katkey | 2068842 |
|---|---|
| _version_ | 1820806310149488640 |
| any_adam_object | |
| author | Bichteler, Klaus |
| author_facet | Bichteler, Klaus |
| author_role | aut |
| author_sort | Bichteler, Klaus |
| author_variant | k b kb |
| building | Verbundindex |
| bvnumber | BV042421833 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)724768941 (DE-599)BVBBV042421833 |
| dewey-full | 515.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7 |
| dewey-search | 515.7 |
| dewey-sort | 3515.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-0055-6 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>04278nam a2200661zc 4500</leader><controlfield tag="001">BV042421833</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1998 xx o|||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783034800556</subfield><subfield code="c">Online</subfield><subfield code="9">978-3-0348-0055-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783034800549</subfield><subfield code="c">Print</subfield><subfield code="9">978-3-0348-0054-9</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-3-0348-0055-6</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)724768941</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042421833</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.7</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Bichteler, Klaus</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Integration - A Functional Approach</subfield><subfield code="c">by Klaus Bichteler</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Basel</subfield><subfield code="b">Springer Basel</subfield><subfield code="c">1998</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (VIII, 197 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Modern Birkhäuser Classics</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">This book covers Lebesgue integration and its generalizations from Daniell's point of view, modified by the use of seminorms. Integrating functions rather than measuring sets is posited as the main purpose of measure theory. From this point of view Lebesgue's integral can be had as a rather straightforward, even simplistic, extension of Riemann's integral; and its aims, definitions, and procedures can be motivated at an elementary level. The notion of measurability, for example, is suggested by Littlewood's observations rather than being conveyed authoritatively through definitions of (sigma)-algebras and good-cut-conditions, the latter of which are hard to justify and thus appear mysterious, even nettlesome, to the beginner. The approach taken provides the additional benefit of cutting the labor in half. The use of seminorms, ubiquitous in modern analysis, speeds things up even further. The book is intended for the reader who has some experience with proofs, a beginning graduate student for example. It might even be useful to the advanced mathematician who is confronted with situations - such as stochastic integration - where the set-measuring approach to integration does not work. ------ Reviews This book provides a complete and rapid introduction to Lebesgue integration and its generalizations from Daniell’s point of view, (…) The development is clear and it contains interesting historical notes and motivations, abundant exercises and many supplements. The connection with the historical development of integration theory is also pointed out. - Zentralblatt MATH The material is well motivated and the writing is pleasantly informal. (…) There are numerous exercises, many destined to be used later in the text, and 15 pages of solutions/hints. - Mathematical Reviews</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functional analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functional Analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Riemannsches Integral</subfield><subfield code="0">(DE-588)4049996-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Maßtheorie</subfield><subfield code="0">(DE-588)4074626-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Integrationstheorie</subfield><subfield code="0">(DE-588)4138369-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Integration</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4072852-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Lebesgue-Integral</subfield><subfield code="0">(DE-588)4034949-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Maßtheorie</subfield><subfield code="0">(DE-588)4074626-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Integration</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4072852-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Integrationstheorie</subfield><subfield code="0">(DE-588)4138369-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="8">3\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="3" ind2="0"><subfield code="a">Riemannsches Integral</subfield><subfield code="0">(DE-588)4049996-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="3" ind2=" "><subfield code="8">4\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="4" ind2="0"><subfield code="a">Lebesgue-Integral</subfield><subfield code="0">(DE-588)4034949-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="4" ind2=" "><subfield code="8">5\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-3-0348-0055-6</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">3\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">4\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">5\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027857250</subfield></datafield></record></collection> |
| id | DE-604.BV042421833 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-24T04:23:24Z |
| institution | BVB |
| isbn | 9783034800556 9783034800549 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857250 |
| oclc_num | 724768941 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (VIII, 197 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer Basel |
| record_format | marc |
| series2 | Modern Birkhäuser Classics |
| spellingShingle | Bichteler, Klaus Integration - A Functional Approach Mathematics Functional analysis Functional Analysis Mathematik Riemannsches Integral (DE-588)4049996-0 gnd Maßtheorie (DE-588)4074626-4 gnd Integrationstheorie (DE-588)4138369-2 gnd Integration Mathematik (DE-588)4072852-3 gnd Lebesgue-Integral (DE-588)4034949-4 gnd |
| subject_GND | (DE-588)4049996-0 (DE-588)4074626-4 (DE-588)4138369-2 (DE-588)4072852-3 (DE-588)4034949-4 |
| title | Integration - A Functional Approach |
| title_auth | Integration - A Functional Approach |
| title_exact_search | Integration - A Functional Approach |
| title_full | Integration - A Functional Approach by Klaus Bichteler |
| title_fullStr | Integration - A Functional Approach by Klaus Bichteler |
| title_full_unstemmed | Integration - A Functional Approach by Klaus Bichteler |
| title_short | Integration - A Functional Approach |
| title_sort | integration a functional approach |
| topic | Mathematics Functional analysis Functional Analysis Mathematik Riemannsches Integral (DE-588)4049996-0 gnd Maßtheorie (DE-588)4074626-4 gnd Integrationstheorie (DE-588)4138369-2 gnd Integration Mathematik (DE-588)4072852-3 gnd Lebesgue-Integral (DE-588)4034949-4 gnd |
| topic_facet | Mathematics Functional analysis Functional Analysis Mathematik Riemannsches Integral Maßtheorie Integrationstheorie Integration Mathematik Lebesgue-Integral |
| url | https://doi.org/10.1007/978-3-0348-0055-6 |
| work_keys_str_mv | AT bichtelerklaus integrationafunctionalapproach |